Algebra worksheet — GCSE Foundation

1.y = x + 10. Work out the value of y when x = 0.

2.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

3.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

4.Work out the value of 3x² − 4x when x = −2.

5.Solve the inequality 9 − 2x ≥ 1.

6.Write down the gradient of the line with equation y = 7x − 2.

7.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

8.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

9.A number machine multiplies its input by 5. Work out the output when the input is −1.

10.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

11.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

12.y = 5 − 2x. Work out the value of x when y = 11.

13.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

14.Write down the expression that means 5 more than half of n.

15.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.